Yes, I've memorized them. You should, too! If 1 minute equals 60 seconds and it does , then. The fact that the conversion can be stated in terms of " 1 ", and that the conversion ratio equals " 1 " no matter which value or unit is on top, is crucial to the process of cancelling units.
I have a measurment in terms of feet per second; I need a measurement in terms of miles per hour. To convert, I start with the given value with its units in this case, "feet over seconds" and set up my conversion ratios so that all undesired units are cancelled out, leaving me in the end with only the units I want. They gave me something with "seconds" underneath so, in my " 60 seconds to 1 minute" conversion factor, I'll need the "seconds" on top to cancel off with what they gave me.
This will leave "minutes" underneath on my conversion factor so, in my " 60 minutes to 1 hour" conversion, I'll need the "minutes" on top to cancel off with the previous factor, forcing the "hour" underneath. Since I want "miles per hour" that is, miles divided by hours , things are looking good so far. They gave me something with "feet" on top so, in my " feet to 1 mile" conversion factor, I'll need to put the "feet" underneath so as to cancel with what they gave me, which will force the "mile" up top.
This is right where I wanted it, so I'm golden. By setting up my conversion factors in this way, I can cancel the units just like I can cancel duplicated factors when I multiply fractions , leaving me with only the units I want. Then I do the multiplication and division of whatever numbers are left behind, to get my answer:. How did I know which way to put the ratios? How did I know which units went on top and which went underneath? I didn't. Instead, I started with the given measurement, wrote it down complete with its units, and then put one conversion ratio after another in line, so that whichever units I didn't want were eventually cancelled out.
If the units cancel correctly, then the numbers will take care of themselves. By making sure that the units cancelled correctly, I made sure that the numbers were set up correctly too, and I got the right answer. This "setting factors up so the units cancel" is a crucial aspect of this process. Simply pick a fraction with the desired units km on top and the given units mi on the bottom:. As you see, you can use either conversion factor, miles to kilometers or kilometers to miles.
Rule 2 in picking a fraction , as originally stated, only applied when the units to be converted were in the top of the fraction or not in a fraction at all. If the original measurement had the given units on the top, your 1-fraction will have them on the bottom; but if the given units are on the bottom of the original measurement then your 1-fraction must have them in the top.
Do this so that you can divide top and bottom by the given units when simplifying. Sometimes you have to deal with squared units.
But they are actually easier to manipulate if you treat them just like variables again! I correspond with a friend outside the US, and we are describing our homes to each other. If my apartment measures square feet, what is that in square meters? What about cubic measure? How many cubic feet is 12 cubic yards? In a nutshell, do all conversions of units by multiplying the original measurement by a well-chosen form of the number 1.
A bit less briefly:. Find the conversion factor for the given and desired units, and write it as a fraction with the given units in the opposite position from the original measurement. If the original measurement has the given units in the numerator, the conversion fraction needs them in the denominator, and vice versa. The value of that fraction is 1, since the top and bottom are equal. If the given units are raised to a power, raise the conversion fraction to that same power. Multiply the original measurement by the conversion fraction, and simplify.
You can also use these same techniques to do currency conversions, which are probably not on your calculator because the rates fluctuate.
See the practice problems. The currency convertor at xe. The reason is that the two measures have different zero points. What do I mean by that? But with temperature this is not true: 0 degrees C is a different temperature from 0 degrees F.
You may recognize this as the slope-intercept form of the equation of a straight line. Temperatures take special caution because of differing zero points , but at least temperatures can be converted.
However, some conversions are completely impossible , not just impossible using the techniques on this page but impossible by any means at all. Why is that? Because gallons and liters measure volume, and square feet or square centimeters measure area. You can use dimensional analysis to show this in a formal way, but informally just remember that area is two dimensions of length and volume is three dimensions of length, and measurements you convert must always have the same number of dimensions.
Here are some problems to practice on, with the conversion factors you need and my answers. You should be able to do all of them easily by using the techniques on this page.
Remember not to make your answers more precise than the original measurements! If you run into trouble, or if you get a different answer and after careful checking it still looks right to you, you might post a note to the newsgroup alt. The Introduction asks which is faster, 60 miles an hour or 60 feet a second. How much does a 2-liter bottle of soda pop weigh in pounds? An Englishman returning home from Norway has kroner of pocket money that he never spent. How much is that in pounds?
Assume an exchange of NOK How high was the cliff, if the rope nearly reached the bottom? Conversion rate optimization , or CRO, is the process of improving your conversion rate. It helps to identify which elements on your ads and pages optimize your online conversion rate. For example, you might test different headlines, buttons, calls to action, or images on your landing pages to see which variations lead to more conversions. Our software and services help businesses and agencies take the guesswork out of pay-per-click advertising so you get more from your marketing budget.
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